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An optimal control problem in polyconvex hyperelasticity

Title data

Lubkoll, Lars ; Schiela, Anton ; Weiser, Martin:
An optimal control problem in polyconvex hyperelasticity.
In: SIAM Journal on Control and Optimization. Vol. 52 (2014) Issue 3 . - pp. 1403-1422.
ISSN 0363-0129
DOI: https://doi.org/10.1137/120876629

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Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
DFG Research Center Matheon "Mathematics for key technologies"FZT 86

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We consider an implant shape design problem arising in the context of facial surgery. The aim is to find the shape of an implant that deforms the soft tissue of the skin in a desired way. Assuming sufficient regularity, we introduce a reformulation as an optimal control problem where the control acts as a boundary force. The solution of that problem can be used to recover the implant shape from the optimal state. For a simplified problem, in the case where the state can be modeled as a minimizer of a polyconvex hyperelastic energy functional, we show existence of optimal solutions and derive---on a formal level---first order optimality conditions. Finally, preliminary numerical results are presented for the original optimal control formulation.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: A preliminary version is published in the ZIB Reports 12-08 (2012).
Keywords: polyconvex elasticity; implant design; optimal control
Subject classification: Mathematics Subject Classification Code: 49J20 (74B20 65N21 65N30).
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 02 Feb 2015 12:35
Last Modified: 19 Mar 2015 11:43
URI: https://eref.uni-bayreuth.de/id/eprint/6114